You deposit 200 at the end of every month into an account pa

You deposit $200 at the end of every month into an account paying nominal annual interest of 3% convertible monthly. This continues for three years, upon which the nominal rate changes to 2% and you increase your contribution to $250 per month. How much money is in the account after a total of five years, i.e., at the time of your 60th deposit?

Solution

First we have to find compound amount for 3 years

in this priciple amount is P = $200 , Interest rate per period is i = 3% = 0.03

and the number of compound period is n= 3

compound amount is

A = P(1+i)ⁿ

= 200 (1+0.03)³  = 218.5454

now find the compound amont for 2 years

The principle amount P = $250 , interest rate per period i = 2% = 0.02

and the number of compounding period n = 2

   A = P(1+i)ⁿ

  = 250 (1+0,02)² = 260.1

now we have to find the simple interest on amount 218.5454 for 2 years

I = P .r. t

= 218.5454 (0.02)(2) = 8.741816

therefore

Total amount = compound amount for 3 years + compound amount for 2 years + interest on compound amount of ears for 2 years

= 218.5454 + 8.741816 + 260.1

= 487.387216

After 5 years deposited $418.387216 in account

Done